Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.

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6
votes
2answers
152 views

NDSolve and matrix formulation do not produce the same result. Why and which is more precise?

Let's assume a vector of variables $\vec a=(a_1(t),a_2(t),a_3(t))$ and let's assume a following DE$$C\ddot{\vec a}=B\dot{\vec a}+A\vec{a}+\vec F.$$ If $A$ and $C$ are both reversible, than the DE can ...
20
votes
2answers
357 views

Numerical optimal control

I was hoping to tackle optimal control using Mathematica in order to learn how I can use Mathematica's built in numerical integration and optimization functions together in order to solve an optimal ...
0
votes
0answers
36 views

Solving a system of Coupled ODE encounter problem “there is a dependent variable does not appear in any equation” [on hold]

I am solving a system of non-linear coupled ODE, but Mathematica reports that "There is an equation that involves none of the dependent variables or there is a dependent variable that does not appear ...
-2
votes
1answer
54 views

Nonlinear system of ODEs need phase-plane

I have this system of equations : I need to solve this equation for different parameters, for now theta is 1, alpha is 25 and ...
0
votes
1answer
44 views

Failed to extract parameters by fitting data with ODE

I'm trying to extract 4 parameters by fitting one set of data with an ODE via NonlinearModelFit. I originally thought the process should be straightforward, but later on I found I was totally wrong. ...
0
votes
1answer
52 views

NDSolve Unable to continue with complex values or beyond floating-point exceptions error

Initially tried to solve following first degree of differential equations using following method ...
0
votes
0answers
41 views

Solving system of ordinary differential equations where coefficients are matrices

I am attempting to use NDSolve to solve a system of ordinary differential equations defined by matrices. Here's the setup of my problem and what I have tried so far. I'm interested in applying the ...
2
votes
0answers
47 views

Unusual error message from Solve when called by DSolve

Question 111150 presents an equation nonlinear in its leading derivative ...
3
votes
2answers
216 views

Is there is a decreasing function that fits my data?

Cross-posted in http://tieba.baidu.com/p/4440556337 http://tieba.baidu.com/p/4440547130 I was wondering if there is a function that fits the following data perfectly or properly. There is a ...
0
votes
1answer
63 views

Sum the several solution functions returned by DSolve [duplicate]

Could you please explain why this code does not work. ...
0
votes
0answers
38 views

fit multiple dataset with a single ODE to extract parameters

I found my problem very similar to the one discussed in here. But I'm having difficulties to fit multiple dataset (with varied temperatures) to a single ODE. The hurdle for me now is since the rate ...
8
votes
1answer
116 views

Beam deformation due to localized force distribution

I would like to simulate the deformation of a beam which is fixed on one end and has some localized forces applied along the top. I have been inspired by this Mathematica example: ...
1
vote
0answers
63 views

Solving two PDEs (for f[x,y] and g[x,y]) coupled through a non-linear function |Grad[f[x,y]]|^2

I am new to Mathematica, trying to solve two PDEs (for f[x,y] and g[x,y]) coupled through Grad[f[x,y]]. In the following code when n is set to 1, NDSolve seems to be able to solve for f[x,y] and ...
2
votes
1answer
72 views

Problem with 3rd order ODE solution from DSolve

I Dsolved the following 3rd order ODE: x'[t]==(3x''[t]^2-Sqrt[9x''[t]^4+4x'''[t]^2])/(2x'''[t]) Mathematica (version 8) gave me three solutions including the ...
1
vote
1answer
57 views

How to rescale a NDSolve curve to fit in a box?

I'm numerically solving some differential equations and the 3D curve I get has a very complicated shape and size that cannot be predicted from the initial conditions. I need to rescale the whole ...
0
votes
1answer
71 views

Solve the n ODE in the loop, add the solutions to create one function

I need to solve the n ODE and create a function which is a sum of all the solutions. I wanted to use the code below, but only part (solve) and (create solution) works well. How can I store the ...
2
votes
1answer
121 views

The numerical solution of a nonlinear ODE: boundary value problem

I want to solve the following nonlinear ordinary differential equation with boundary values $f(0)=1$ and $f(1)=1$: $${\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}f \left( x \right) ={\dfrac { \left( 51-51\,x ...
2
votes
2answers
72 views
1
vote
2answers
83 views

A way to show all the 3D curve, with view still centered on {0, 0, 0}

I frequently have this graphics output problem : I draw a 3D curve using NDSolve, and depending on the initial data, there's no way I could predict the shape and ...
4
votes
3answers
649 views

Does it mean that there no analytical solution if Mathematica cannot find analytical solution?

I'm solving simple but coupled ODEs recently. I use both MATLAB symbolic computation and Mathematica. For example, my coupled ODE is the following \begin{align*} &\dot{x}(t)=y(t)-\rho ...
1
vote
1answer
70 views

Variable coefficient Differential Equation

Can anyone help with the following differential equation. The errors i am getting are also given. ...
1
vote
1answer
92 views

Solve a system of nonlinear ODE

I have a set of coupled non-linear ODEs, they look symmetric. But when I use matlab symbolic calculation to solve, matlab told me that no explicit solution found. I was recommended by my friend to try ...
0
votes
1answer
58 views

NDSolve and a vector function [duplicate]

I'm trying to solve a set of differential equations which include a numerical function that takes a vector and returns a vector. ...
2
votes
1answer
115 views

Improving the speed of evaluating numerical solution to a sytem of PDE

I am running a simulation for a kinetic reaction inside a pellet modeled by a system fo reaction-diffusion equations. ...
1
vote
1answer
54 views

How to define “DiffusionCoefficients” in InitializePDECoefficients that depend on ElementMarker?

Modelling a Poisson Equation on piecewise constant material, ElementMarkers on the PointElements are used for the boundary ...
3
votes
2answers
245 views

Why can't FindFit get the proper result in this problem?

Cross-posted in http://tieba.baidu.com/p/4425634583 The mathematica helps me solve one differential equation in numerial method and got the data of the answer,but the taylor series fit is not good in ...
0
votes
1answer
52 views

Reduce in NDSolve [duplicate]

Second order ode; neither the trig RHS simplifies nor is the solution obtained readily: ...
1
vote
0answers
49 views

How to use interpolating functions in NSolve with a piecewise function?

I have a system of two non-linear differential equations that are piecewise, the solutions of which I would like to use to obtain the values of a third variable that is also piecewise. I have trouble ...
1
vote
1answer
113 views

Problem with solving a system of differential equations [closed]

I am trying to reproduce a result that is part of a derivation of the flow due to a rotating disk. I have as given this system of differential equations. (In these equations primes indicate ...
0
votes
0answers
46 views

ndsz : step size is effectively zero; singularity or stiff system suspected

This is the first time I ask a question. I have seen many solutions to this error and tried but they are not working. Here is the code. Needs["DifferentialEquations...
0
votes
0answers
46 views

Output of NDSolve is useless when the system gets bigger

I have a bridge, which I want to discretize on $n$ stiff rods. To find a solution I wrote the following code in mathematica: ...
3
votes
0answers
53 views

EvaluationMonitor slows down NDSolve considerably

Hi guys I'm solving a nonlinear system of ODEs with NDSolve. Since the dimension of the system ranges from 2700 to 20000 equations, depending on the parameters, the time required to solve the entire ...
-3
votes
1answer
78 views

How to implement Bifurcation of delayed Lorenz system? [closed]

The delayed Lorenz system is as follows: (Bifurcation parameter as $\tau$) $$\begin{align*} D^\alpha x_1(t) = & a_1(x_2(t-\tau)-x_1(t)) \\ D^\alpha x_2(t) = & a_2x_1(t)-x_2(t)-x_1(t)x_3(t) ...
5
votes
1answer
81 views

Passing starting values to FindRoot when called by the Shooting Method of NDSolve

According to the documentation of the NDSolve Method -> "Shooting" option, it is possible to pass to ...
0
votes
0answers
87 views

NDSolve with default settings solves much faster than classic Runge-Kutta 4

NDSolve with default parameters takes 0.25 s for the first run. With Runge Kutta 4 specified, it takes about 4.6 s, ...
0
votes
0answers
64 views

How to systematically approach when solving a large system of differential equations?

I defined several functions in order to get to the final system of a partial differential equations I have to solve. Here is how I did those definitions: ...
0
votes
1answer
79 views

Proper way to produce StreamPlot

I have faced with problem of not completely correct phase trajectories of ODE, which was produced by StreamPlot. Next following code ends up with this plot: ...
3
votes
0answers
54 views

Singularity treatment in a simple problem [duplicate]

With a simple search, several posts can be found on treating singularities encountered while using NDSolvefamily of numerical methods. However, most of them involve ...
1
vote
1answer
69 views

Discontinious Boundary condition NDsolve

Assume we have any PDE to be solved on the rectangular domain $0<X<4$ and $0<y<2$ How do we tell Mathematica to impose the following boundary conditions? $U[0,y,t]=0, if, 0<y<1, ...
1
vote
2answers
64 views

If statement, differential equation

I've got problem with If statement. It doesn't work. I've never used Mathematica before, probably it's a problem with syntax. ...
1
vote
0answers
34 views

wrong sign with NeumannValue

I want to use NDSolveValue with Neumann boundary condition. The documentation says this https://reference.wolfram.com/language/ref/NeumannValue.html . In the ...
1
vote
2answers
232 views

Differential equation and For loop in Mathematica

I'm trying to optimize some kind of process in Mathematica. I did it without any problems in Matlab and now I'm trying to do the same in Mathematica which I don't know at all. I'm trying to find the ...
1
vote
1answer
76 views

How to plot an Ordinary differential equations

Hey guys I'm using mathematica 5 now, and so new to this software thing. May I know how to plot the direction field using PlotVectorField[] and also finding ...
1
vote
0answers
40 views

NDSolve with (approximately continuous) Piecewise input

I am finding some troubles when using NDSolve with this piece of code: ...
0
votes
1answer
30 views

WhenEvent StopIntegration not working [closed]

I am trying to use a WhenEvent to StopIntegration when Tmelt=1356 is reached. Although the NDSolve appears to be working, "StopIntegration" is not stopping the integration and no value is given for ...
3
votes
1answer
68 views

NDSolve with an interpolating function in Piecewise

Again I have question I hope someone can answer. I made a very simple example illustrating my more difficult problem. I want to solve a differential equation numerically with a conditional in the ...
3
votes
4answers
217 views

Stiff coupled system of ODE's

I am having trouble with a possible stiff nonlinear system of ODE's. ...
0
votes
1answer
97 views

NDSolve coupled Non Linear differential equation, Obtain solution

Trying to solve a coupled differential equations of motion. When there is no Working Precision mention it runs and give following plot for θ[t] but this is wrong, θ must be symmetric about 0. ...
0
votes
0answers
25 views

Discretization of a region for NDSolve using [duplicate]

I would like to mesh the region below in order to use it for a calculation by means of NDSolve. Could anyone help me to discretize this region for NDSolve using. Thank you very much. ...